Development of concrete complicated control processes models, development of corresponding computer simulation systems and computer simulation complex, development on its basis of means of planning, projection, control supporting procedure are foundation of theoretical and metrological investigation are carrying out in the department. Below are described some models of concrete complicated processes, computer simulation systems and computer simulation complex which are produced on the basis of this models, characterized results of investigation, obtained with the use of simulation experiments.

1. Together with specialists of Automatic Systems Research Institute the model of process of projection, production and exploitation of technical system used in industry was developed. Simulation system was created on the basic of the model for supporting of procedure co-ordination of technical system product, spare parts product, capacity remount service and other support system of exploitation process. Some result of the investigation is published in

2. Intention to create wide-ranging anti-missile system with elements of cosmic base had been declared by president of USA R. Ragan 23 March 1983. This intention was called strategic defense initiative (SDI). In 1984-1986 in the department together with the specialists from MOM, the investigations of effectiveness and technical marketability of SDI were carried out. In the framework of this investigation several models of episode of cosmic war had been developed. One of them was the model of action of brilliant pebbles system (BPS). Idea of BPS is to form orbital grouping of many (100000) light inexpensive rocket (this rocket was called 'brilliant pebbles') with infra-red guidance system. This rockets are able to intercept intercontinental ballistic rocket on active part of its trajectories. Interactive computer simulation system was developed with use of instrumental simulation system MISS on basis of the model. It was demonstrated with use of simulation experiments that brilliant pebbles anti-missile system incapable to defend of massive intercontinental ballistic rocket attack. Some result of the investigation was published in:

3. Together with history specialists had been developed model of economic dynamics of ancient Greek town at the time of Peloponness war 431 - 404 B.C.. The follow ideas was in the basis of the investigation. There is structure of mathematical models now, which describe various aspects of modern economics. Nevertheless modern economics as a whole is complex process and economics development prognosis are making by 'humanitarian' specialists. But Ancient Greek economics as a whole of Peloponness war period is much simpler than modern one: nomenclature of goods was of order several tens, but not several tens million as now, production and consumption structures was stable during century but not transform every day as now, money was not still article of trade and so on. Therefore it is possible to try to simulate by mathematical model Ancient World economic dynamic in some period in some 'closed' in economics sense region, i.e. simulate production, consumption processes, process of market exchange of goods. Therefore there is hope to reproduce economy dynamic of town-states of Ancient Greek. The outer characteristics of described mathematical model are population number in the town-states, population distribution on social groups in every state, production structure, consumption structure of various social groups, production efficiency, prices. The inner characteristics are temporal dynamics of social groups, money and goods. Hypothesis about invariance which is the models basis is independence of production structure, production efficiency in the period under consideration from temporal dynamics of social groups, money and goods. As for prices, they were very stable in Ancient Greek in very long period, which include period of Peloponness war. Only excluded circumstances, connected with armed conflict, may induce prices variation. Influence of armed conflict on economics was 'outer' in the model and therefore prices variation was considered also as 'outer' factor, in spite of evident dependence prices variation from temporal dynamics of social groups, money and goods. The same concern peoples number in the town-states, peoples distribution on social groups in every state.

It is enough evident that having information about Ancient World economics of any period in any region is insufficient to identify corresponding mathematical model. But there are many other knowledge about various aspect of human life of Ancient World not only about economics. Various aspects of human life are connected with each other and with economics. The experts which have some ideas about relationship between economics and other ancient world human life aspects may to try to fulfill reconstruction of some historical period in some region in the follow manner. The mathematical model of economy dynamic of the region in the period may by compose and its outer characteristics may be choose so that corresponding economy dynamics 'do not contradict' all other information about the region in the period. May or not to fulfill such investigation depend on the region, the period, the expert.

If some expert will have the courage to carry on such investigation and if he will have obtained the results, which he will be satisfied then the 'new information' (indeed hypothesis of the experts about values of the outer characteristics of the mathematical model of economy dynamics and economy dynamics itself) will be extract from the experts ideas about relationship between economics and all other known aspects of human life in the region in the period, which are known to the expert. The economy dynamics mathematical model will be only instrument of 'new knowledge' extraction. This manner of 'new knowledge' extraction is illustration of technology which unify mathematical and humanities methods of investigation real phenomena (processes/systems).

In the accordance with described ideas the mathematical model of the economy dynamics of town-states in Ancient Greek in the Peloponness war period 431-404 B.C. was composed. Only five town-states was described in the model: Athens, Sparta, Phivy, Siracuzy, Korinf. In the basis of described mathematical model was every town-states population division into 15 social group including state (state was participant of economy processes) and goods division into 12 kinds, including slaves (slaves is interpreted not as social group, but as a kind of goods). The mathematical models outer characteristics was number of people in every social group in every town, agricultural social group plot of arable land area and its crop capacity, craftsman productivity of labour, various social groups consumption goods norms (including slaves). Goods prices was outer characteristics of the model. The mathematical models inner characteristics was amount various goods and amount of money which every year of 431-404 B.C. period every social group had been possessed.

In the mathematical modeling equations basis was arithmetical calculation (no mathematical means except arithmetical means was used) of social groups amounts goods and money in every year of 431-404 B.C. period. Many various circumstances which influenced economics was took into account as outer factors. Namely, it was took into account silver output by states slaves (in Athens) resulting in input money in town-states systems, the war expenditure, war plunder, pillage in the course of a town siege and agricultural towns social groups going off their plot of arable land in the town and so on.

The matter of the investigation with mathematical point of view was the mathematical model identification, i.e. mathematical models outer characteristics determination. It was two parts in the investigation. The first part was connected with restoration town-state systems economy in the initial year of 431-404 B.C. period when Athens-Sparta war do not start. It was the end of economy and political stability period of the Ancient Greek town-state systems. Equality between income and consumption of lowest social groups was the basis of first part of investigations. This equality resulted from town-states systems economy stability in the period preceded the Peloponness war and resulted in the relations between set of outer characteristics values

The first part of the investigation may be characterized as static systems analysis of the information about the Peloponness war period of the Ancient Greek History. Initial values of inner characteristics of the models had been determined from the static analysis. The investigation second part in comparison with the first part may be characterized as dynamic system analysis of information about Peloponness war period Ancient Greek History . The economy dynamics had been reproduced and the outer characteristics had been corrected such that the economy dynamics 'did not contradict' all other information about Ancient History period under consideration.

Dynamic system analysis of information about Peloponness war period Ancient Greek History may be illustrated by follow example. It is known the rhyme of Ancient Greek writer Aristophan. A son ask his father: ``Oh, my father if the judges do not sit down into Geliee, where you find money for us to our breakfast, to our supper or into water by your had?'' The father reply: ``God see, I don't know.'' The rhyme describe desperate plight of poor agricultural social groups in Athens in the course Archidam war. Sparta tsar Archidam besieged Athens in 431, 430, 428 B.C. Athens stand the sieges, but countryside around Athens was plundered and many countrypeople crowded in the town. Such peoples of poor agricultural social group had no input and look for casual earnings. One of such earnings was participation in the capacity of judge in Athens court (Geliee) as the participation was paid. Every morning peoples who wanted be judges gathered in front of the Court and if they were too many, lots had been thrown. It is exactly known that day pay for participation in Court was 2 obol (one of monetary unit in the Acient Greek). It is exactly known that in the course of Archidam war the pay was increased to 3 obol. Thus the rhyme contain information about subsistence minimum (2 obol) for family of 3-4 persons and prices increasing in the course of Archidam war. There is illegibility of course in this relations but described circumstances are not single. All such circumstances in various moments of the period under consideration, if they concern economics, is connected by mathematical model and permit to do some hypothesis about values of characteristics, which are not known from original sources.

Described investigation do not pretend on some new results in History but only on illustration interaction possibility between mathematical and humanities methods of investigation real phenomena (processes, systems). The interaction may be will produce new results in History only when mathematical model will be realized in the form of interactive simulation system, accessible any expert and will be possible to test any hypothesis about values any characteristics and to restore logic way with use of which the values was obtained.

4. System of several states was the object for modeling in the department in the period 1966-1996. Economy dynamics and armed conflicts if they took place were described by mathematical models. Every state territory was divided in the model into regions. Every region was characterized by basic fund of industry in civil and war sectors, amount of arming (models inner characteristics), efficiency of the funds (models outer characteristics). Product of fund of industry civil sector of every states is divided into consumption of states population, investment in civil and war sectors in every region and various expenditure, connected with relation between states. The funds variation was determined by natural amortization and investment. War sector of states economy produced weapons. Variation of weapons amount was determined by natural amortization and productive capacity of war sector. Armed conflicts was described by simplest so called Lanchester model. Psychological factor had been took in to account. This factor had been expressed by introducing 'L.N. Tolstoi factor' (see lower). Several variants of the model and corresponding computer simulation system had been developed. This investigations had been supported various state and private institutes.

The investigations was carried out by the simulation games method. Government of every state had been presented by group of persons. This groups made decision about distribution of industry civil sector product upon consumption, investment in economy sectors and other expenditure, about distribution of weapons produced by war economy sector on regions, about relation with other states. Information which possess every state about economy, armament, intention, purpose each other, was formed in process of simulation games by special group of experts --- supervision of games in the accordance with purpose of investigations. The states purposes itself also was assigned by supervision of games.

Virtual world was arose sometimes in the process of simulation games. This virtual world was organism, which had contained inside self-preservation mechanisms and self-destruction mechanisms (i.e. arising war in states system). This mechanisms was connected tightly with relationship system between states. It turns out for instance that it was impossible to assign purpose to states: states purposes depended on relationship system between states, arouse hierarchy of purpose and assigned purpose was only element of the hierarchy. The virtual world was of course different from real world, but observation the virtual world and comparison with the real one permits to see relations and circumstances which to see for no particular reason is very difficult.

One of such circumstances was arising of war in the world, where every state had assigned purpose to increase consumption of people and had no urge to deadly quarrel. At the bottom of such situation was lack of trustworthy information, which states possess about other states. Armament race had arose in the states system if states had no trustworthy information about war sector of industry, about weapons each other. States system had got very unstable, if one of state had wrong information about intention and purpose of other states. Practically inevitably war had arose in the states system if all states had wrong information about intention and purpose of other states despite of no state had purpose to war. On the country disarmament race had arose often in the states system if states had trustworthy information about war sector of industry and about weapons each other and was quite confident that other states had no aggressive designs. Mechanism of the disarmament race was very simple. It is known and it was took into account in the model of armed conflict that defense demand less weapons then attack and for instance, if two states have equal amount of weapons with equal efficiency and no state have no aggressive designs, then one of states may decrease defense expenditure without decreasing own safety. In this case the state will have advantage in economy development and it will be reason for another state also to decrease defense expenditure.

Of course it is only rough schemes of real situations and circumstances. In the same way as for model of economy dynamic of town-states in Ancient Greek, the result of described model do not pretend on some specific conclusion in some specific field and extraction is illustration of technology which unify mathematical and humanities methods of investigation real phenomena (processes/systems): composing and studying such schemes, arising their structure is one of instrument which may be used for organizing self-preservation mechanisms of the world and suppressing its self-destruction mechanisms. Some result of the investigation was published in:

Pavlovsky Yu. N. Methods of Simulation Games in the Problem of Geopolitics, Safety, States Relationship. Materials of Constituent Assembly of Russian Society of Operation Research. Moscow. CCAS. 1997. PP. 44-56.

5. Together with several organization of Department of Defense of USSR had been developed mathematical models of operation of modern armed forces on land seat of war in scales battalion - regiment - division - front. Operation of modern armed forces had been treated as totality of simultaneous, heterogeneous, tightly interconnected processes: process of mutual annihilation, process of transference, process of material and technical support, information process (information gathering, storage, transfer, processing), process of decision making in operating control. Corresponding computer simulation systems had been developed and simulation experiments had been conducted. One of methodological result of the investigation is the follow. Armed forces of every state have 'inner structure': combativity and relationship between type of armament in the framework of which control of armed forces is possible. 'Normal' operation of armed forces is took place until the inner structure of armed forces is preserved. Therefore main problem of control of armed forces is to preserve own armed forces inner structure. As this problem is the problem of both opponents, normal operation of armed force has aspect of 'mutual agreement'. When one of opponents can not preserved own inner structure then abnormal phase of operation of armed force (as a rule) have been begun (partisan warfare, terrorism). Examples are: USA in Vietnam, USSR in Afghanistan, USA in Iraq.
Some result of the investigation was published in:

6. Together with specialists of the Chair 'Sustainable Development' of State Chemistry - Technology University mathematical model have been developed meant for study some aspects of Sustainable Development problem. Demography, economic, ecological processes have been described by this model in the period commensurable with duration of generation life. Follow of activities types have been treated as branch of production: fundamental science, applied science, outputting, goods production, health protection, education, information gathering, storage, transfer, processing, ecology (production of environment parameters), production of cultural wealth (religion, culture, art). New knowledge are produced by fundamental science, new technologies are produced by applied science with use of the new knowledge produced by fundamental science, natural resources are prepared to using in production by outputting, coefficients of birthing and death are produced by health protection. Humanitarian analysis sustainable development problem have been carried out with use of models languages means. Computer simulation game have been done to use in education. This computer simulation game have been exploited on the Chair 'Sustainable Development' of State Chemistry - Technology University.
Some result of the investigation was published in: